﻿1016 
  Electromagnetic 
  Hypothesis 
  as 
  to 
  Series 
  Spectra. 
  

  

  boundary 
  will 
  come 
  in. 
  We 
  obtain, 
  however, 
  on 
  the 
  same 
  

   hypothesis 
  the 
  equation 
  for 
  the 
  change 
  of: 
  magnetic 
  force 
  

  

  sin 
  kr 
  / 
  , 
  2 
  \ 
  . 
  2coskr 
  

  

  o 
  o 
  I 
  ' 
  To 
  o~~ 
  T* 
  C 
  

  

  kr 
  

  

  ('-A) 
  

  

  where 
  c 
  is 
  a 
  constant. 
  If 
  this 
  expression 
  is 
  always 
  positive 
  

   its 
  graph 
  will 
  resemble 
  a 
  "damped" 
  sine-curve 
  the 
  smallest 
  

   ordinate 
  of 
  which 
  will 
  be 
  at 
  the 
  point 
  

  

  hr= 
  1-2319 
  ir. 
  

  

  Thus 
  in 
  the 
  neighbourhood 
  of 
  this 
  point 
  the 
  amplitude 
  of 
  

   the 
  magnetic 
  disturbance 
  is 
  smallest, 
  and 
  so 
  of 
  all 
  the 
  

   nodal 
  surfaces 
  

  

  kr= 
  1-4303 
  *r, 
  2-1590 
  w, 
  

  

  it 
  is 
  only 
  at 
  the 
  innermost 
  that 
  an 
  electron 
  will 
  be 
  capable 
  of 
  

   describing 
  a 
  steady 
  orbit. 
  

  

  On 
  Radiation. 
  

  

  We 
  have 
  seen 
  above 
  that 
  all 
  the 
  steady 
  motions 
  are 
  

  

  characterized 
  by 
  the 
  same 
  angular 
  momentum. 
  It 
  remains 
  

  

  to 
  obtain 
  a 
  numerical 
  estimate 
  of 
  this 
  constant. 
  From 
  equa- 
  

   tion 
  (2) 
  we 
  have 
  the 
  angular 
  momentum 
  

  

  m(x 
  2 
  -\- 
  y 
  2 
  )co 
  = 
  5c 
  2 
  ?ft/3I2, 
  

  

  and 
  from 
  equation 
  (3) 
  we 
  have 
  

  

  |/)na 
  2 
  (l-4303) 
  2 
  (^/m) 
  = 
  B 
  (Rydberg's 
  constant). 
  

  

  The 
  density 
  p 
  is 
  unknown 
  but 
  we 
  shall 
  take 
  it 
  to 
  be 
  given 
  

   by 
  the 
  equation 
  

  

  e 
  = 
  4/3 
  . 
  TTpa 
  3 
  . 
  

  

  If 
  the 
  angular 
  momentum 
  is 
  denoted 
  by 
  li/ir 
  and 
  if 
  we 
  

   insert 
  the 
  values 
  

  

  ^ 
  = 
  4-7xl0- 
  10 
  ; 
  a 
  = 
  10- 
  8 
  ; 
  B 
  =3"29xl0 
  15 
  

  

  we 
  find 
  

  

  A= 
  6-8x10" 
  

  

  27 
  

  

  which 
  agrees 
  possibly 
  within 
  the 
  limits 
  of 
  experimental 
  error 
  

   of 
  some 
  of 
  the 
  above 
  quantities, 
  with 
  the 
  value 
  of 
  Planck's 
  

   constant 
  6'5xl0" 
  27 
  . 
  

  

  Some 
  idea 
  can 
  now 
  be 
  formed 
  as 
  to 
  the 
  manner 
  in 
  which 
  

   the 
  radiation 
  is 
  given 
  out. 
  An 
  electron 
  having 
  a 
  frequency 
  

   v 
  will 
  have 
  an 
  amount 
  ln> 
  of 
  kinetic 
  energy. 
  If 
  at 
  this 
  

  

  